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Nonnegative approximations of nonnegative tensors
Author(s) -
Lim LekHeng,
Comon Pierre
Publication year - 2009
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.1244
Subject(s) - mathematics , probabilistic logic , bayes' theorem , decomposition , product (mathematics) , tensor product , approximations of π , combinatorics , bayesian probability , pure mathematics , statistics , chemistry , geometry , organic chemistry
Abstract We study the decomposition of a nonnegative tensor into a minimal sum of outer product of nonnegative vectors and the associated parsimonious naïve Bayes probabilistic model. We show that the corresponding approximation problem, which is central to nonnegative PARAFAC, will always have optimal solutions. The result holds for any choice of norms and, under a mild assumption, even Brègman divergences. Copyright © 2009 John Wiley & Sons, Ltd.